Evaluate. Write your answer in simplified, rationalized form. Do not round.

Question

csc 45°

Answer 1

Using the unit circle or special right triangle, we know that the sine of 45° is $\frac{\sqrt{2}}{2}$. The reciprocal of sine is cosecant, so

$$\csc 45° = \frac{1}{\sin 45°} = \frac{1}{\frac{\sqrt{2}}{2}} = \boxed{\sqrt{2}}$$